1
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language

The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is ____________.

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2
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Change Language

Let $$\alpha, \beta(\alpha>\beta)$$ be the roots of the quadratic equation $$x^{2}-x-4=0 .$$ If $$P_{n}=\alpha^{n}-\beta^{n}$$, $$n \in \mathrm{N}$$, then $$\frac{P_{15} P_{16}-P_{14} P_{16}-P_{15}^{2}+P_{14} P_{15}}{P_{13} P_{14}}$$ is equal to __________.

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3
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Change Language

Let $$X=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$$ and $$A=\left[\begin{array}{ccc}-1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1\end{array}\right]$$. For $$\mathrm{k} \in N$$, if $$X^{\prime} A^{k} X=33$$, then $$\mathrm{k}$$ is equal to _______.

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4
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Change Language

The number of natural numbers lying between 1012 and 23421 that can be formed using the digits $$2,3,4,5,6$$ (repetition of digits is not allowed) and divisible by 55 is _________.

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